UPSC Combined Geo-Scientist, Mains · 2016 · Mains Paper II

Q1(f). Temperature dependence of equilibrium

Question

Deduce the variation of Kₚ with temperature and show that Kₚ is independent of pressure.

dln Kₚ/dT=ΔᵣH°/(RT²); the thermodynamic equilibrium constant depends on temperature for fixed standard states.

Use ΔᵣG°=-RTln Kₚ and the Gibbs–Helmholtz equation [∂(ΔᵣG°/T)/∂ T]ₚ=-ΔᵣH°/T². Substitution gives the van' t Hoff equation.
If ΔᵣH° is approximately constant, ln (K_(p,2)/K_(p,1))=-ΔᵣH°(1/T₂-1/T₁)/R.
For ideal gases, Kₚ=Πᵢ(pᵢ/p°)^νᵢ at equilibrium.

The full model answer

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CoversTemperature dependence of equilibriumChemical equilibrium